Failures

We consider three topics which proved frustratingly resistant to the methods of the old quantum theory up to the point of emergence of the quantum mechanics of Heisenberg and collaborators in late 1925. First, the old theory could not account convincingly for the superfluity of stationary states implied by the existence of the complex multiplets seen in most atomic spectra. Second, the progressively more complicated theories proposed for explaining the splittings of lines in the anomalous Zeeman effect were found to lead inevitably to glaring inconsistencies with the assumed mechanical equations of motion. Finally, there was the problem of the dual spectrum of helium, and even more basically, of the ground state energy of helium, all calculations of which in terms of specified electron orbits gave incorrect results. We relate the tangled history of the efforts to provide a theoretical resolution of these problems within the old quantum theory.